 About 21,800 results  books.google.com When e = 0, the sineGordon equation is completely integrable. Usually in partial
differential equations one can only study the stability of a few very simple
solutions; however, for these integrable wave equations, a representation due to
Peter ... 

 books.google.com Later Kolmogorov, Arnold, and Moser showed that certain qualitative properties
of completely integrable systems persist after perturbation: certain ... More
recently it has been shown that certain nonlinear partial differential equations
such as ... 

 books.google.com The idea of the proof of the sufficiency of the conditions stated in the theorem is to
show that these guarantee that each of the M1 and M2characteristic systems C(I
,dM 1) and C(I,dM 2) has a completely integrable subsystem of rank three. 

 books.google.com Many of the important local properties of surfaces are expressed in terms of
partial differential equations, a famous example being ... which is one of the
prototypical examples of a completely integrable nonlinear partial differential
equation. 

 books.google.com a nonlinear ordinary differential equation is the uniformizability of its general
solution. ... In the Lax pair method one usually asserts that a system of partial
differential equations is completely integrable if it can be deduced as the
consistency ... 

 books.google.com Peter J. Vassiliou, Ian G. Lisle  2000  Preview be completely integrable. By iterating this construction, we obtain a flag of C°(Mn,
R)modules ... c 1(*) c... c 1(1) c I, (5) where I(*) is defined recursively by 1(k) = (1(
k1))(1). The flag (5) is called the derived flag of T. It stabilizes at a C°(Mn, ... 

 books.google.com By restricting to the case N = 1, we recover the elliptical representation of Heun's
differential equation (see (4.3)). It is known that the Inozemtsev model of type
BCN is completely integrable. Namely, there exist N differential operators P1(= H)
,P ... 

 books.google.com Therefore, the system of equations (3) will be completely integrable if and only if
the single differential equation dz = (J) dx + \j/ dy i.e., §dx + \\fdydz = 0 ...(4) is
integrable. We know that the necessary and sufficient condition for the single ... 

 books.google.com In other words, the forms 1 (t),..., n(t) satisfy the linear ordinary differential
equations (1.9). ... that a distribution P is completely integrable if for any point a ∈
M there exists an integral manifold N of P such that a ∈ N and dim N = dim P.
Theorem ... 

 books.google.com Volume 23, 1g86 ON COMPLETELY INTEGRABLE SYSTEMS WITM MIGMER
OR0ER CORRECTIONS Yuji Kodama ABSTRACT. The integrable Mamiltonian
systems with certsin claas of perturbations such as higher order corrections are ... 

 